User:Shaunchen8/sandbox/Graphene helix

The graphene helix has been suggested as a structural model for single-wall carbon nanotubes (SWNTs). In the model, the one-dimensional material is synthesized from the spiral growth of a graphene ribbon, resulting in a helically opened, tube-like structure. It can be compared to ivy growing on a tree in nature, wrapping around a cylindrical object as it grows. So far, the main application for graphene helices is for the composition of single-walled carbon nanotubes (SWCNTs). Graphene helices are not naturally found, instead, they are synthesized in laboratories only.

Graphene helices possesses unique properties such as semi-conductivity, photoabsorptivity, and physicality at a nanometer-sized scale, which can bring possibilities to optimizing technology. It can replace the materials used in anywhere from electronic circuit boards to nano-sized springs. This concept has generated much interest in scientists today.

Research
Lee et. al. studied the unique formation of graphene, which led to evidence for the helix model for SWNTs, which is observed from both the high-resolution transmission electron microscopy (HRTEM) and the scanning tunneling microscopy (STM) in 1993. He concluded that the strain energy of the helical growth of a zigzag or armchair graphene ribbon is just about a quarter that of seamless cylindrical SWNTs. Although the zigzag and armchair structures did not possess supermaterial properties, he was one of the first to learn about the unique properties of SWNTs, and thus, graphene helices in general. He also found that published papers dealing with the theoretical aspects of SWNT growth have misinterpreted effects of distortion on the formation of a graphene helix, because chirality is not a necessary condition for the growth of SWNTs.

The Department of Chemistry at Kyoto University and the Graduate School of Engineering Science at Osaka University synthesized hexa-peri-hexabenzo[7]helicene, a primary substructure of graphene helices, in March 2018. First, they used single-crystal x-ray analysis to determine that the structure had a helix-like geometry. This was completed via homogeneous π-extension and confirming the aromaticity of the graphene helix structure. Because the HOMO-LUMO gap was found to contain a small range, the generation of the hexa-peri-hexabenzo[7]helicene was not easy to replicate. This research showed that each component in graphene helices are capable of possessing supermaterial properties.

Much still needs to learned about the properties of different substructures of the graphene helix.

Current Production
Graphene helices can be produced under the processes: photocyclodehydrogenation (removal of hydrogen atoms by a high-energy light beam) and aromatization. Aromatic molecules, including cyclic structures found in graphene helices, have characteristics including low chemical reactivity and π-stacking (obscure layers of π bonds along each surrounding atom). In order to remove hydrogen atom(s), π electrons around the ring must be delocalized. Using high concentrations of energy, the removal of hydrogen atom(s) is possible. Finally, dehydrogenized graphene atoms can bond with each other to expand the helix chain.

Although possible, the high energy concentrations make graphene helices inefficient to produce, both cost and time-wise.

Physical Properties
Although the two-dimensional composition possesses physical properties that are unique, three-dimensional properties from graphene helices can differ variously.

Elasticity and Mechanical Strength
The atomic stress of individual carbon atoms can be tested by the following equation:

$$ \sigma _{ij} ^\alpha = 1/\Omega _\alpha (1/2m _\alpha v _i ^\alpha v _j ^\alpha + \sum_{\beta=1}^n r _{\alpha \beta} ^j f _{\alpha \beta}^i)$$

where, i and j are components in Cartesian coordinates

$$ \alpha$$and $$ \beta$$ are the atomic indices,

$$ m _\alpha$$and $$ v ^\alpha$$are the mass and velocity of atom,

$$ r _{\alpha \beta}$$and $$ f _{\alpha \beta}$$are the distance and force between the atoms,

$$ \Omega _\alpha$$is the volume of atom.

The mechanical strength of helical graphene can be tested using the following equation:

$$ K = Y\sigma _{eff} \surd \pi a = Y\sigma \cos ^2 \theta \surd \pi a$$

where, Y is a constant that depends on the crack opening mode and the geometry of the specimen,

$$\sigma _{eff}$$is the effective stress normal to the crack,

$$\sigma$$is the tensile stress applied to the SWNTs,

$$\theta$$ is the chiral angle,

a is half of the crack length.

This equation calculates the theoretical tensile strength of components made via graphene helices. Based on repeated calculations, it was found that the tensile strength can range from 20.6 - 47.7 GPa with a change in diameter of 10-30 Å. Due to the diameter of carbon atoms ranging from 10-20 Å, it was discovered that the tensile strength usually stayed in the range of the upper limit of tensile strength.

After a considerable amount of testing, the conclusion was made that graphene helices can withstand great elastic deformations, with tensile strains of up to 1000% without fracturing. Compared the flat, two-dimensional sheets of graphene, graphene helices are approximately six times as strong in ultimate tensile strength, which are able to withstand a maximum of 130 GPa, but at only 0.142 nm in length. This ability makes graphene helices a great candidate for flexiblity tests at the extremities of future material elasticity.

Thermal Properties
Zhan et. al. discovered that graphene helices provide better stability and thickness alignment, which converts into a more consistent thermal radiance across the whole structure. The overlapping between the adjacent layers of the graphene helix proved to generate a higher thermal conductivity than multiple layers of flat graphene sheets during his calculations.

Electrical Properties
Electrical properties of graphene helices vary based on the structural integrity it possesses: armchair, zigzag, and chiral.

When a voltage is applied between two ends of an armchair nanotube, a current will flow similar to that of metals.The armchair formation conducts electricity better any other metal used in electrical wires currently. The zigzag and chiral orientations produce graphene helices similar to those with the properties of semiconductors. They conduct a current when energy or an electric field is applied to the free electrons from the carbon atoms, which is useful in smaller-sized transistors in integrated circuits.

Single-walled carbon nanotubes
Single-walled carbon nanotubes is an example of the application of graphene helices. They exhibit unique electrical properties. The most notable feature is that their band gap can vary from zero to about 2 eV and their electrical conductivity can show metallic or semiconducting behavior. Its excellent conductivity makes these nanotubes a candidate for creating nano-sized electronic components beyond the current scale. Electrical property of SWNTs can be regarded as zigzag, making it a conductor.

There are two current ways for the production of SWCNTs: electric-arc technique (vaporization of graphite with a short pulse, high-powered laser) and laser ablation. However the electric-arc technique was found to be impractical due to the small production sizes. Using pulses of a laser to produce SWCNTs was much more efficient because a minimal amount of carbon soot is created, as opposed to the electric-arc technique. As a result, it deemed to be better in terms of producing a large amount of SWCNTs.

Nano-sized molecular inductor
Because graphene helices have a helical molecular geometry, they have a high probably chance of being used for nanometer-sized molecular inductors, which can induce a magnetic field in nano-sized, helically twisted dimensions and respond to microscopic forces in nano-sized spring materials.

Spin filters
Spin filters created with ferromagnetic metals only have a 50% filtering efficiency, but with graphene’s magnetoresistance, spin polarization can go upwards to an efficiency of about 80%.

Molecular spring materials
With graphene helices, springs both offer the material stiffness and high deformity due to the mechanical properties described. Microscopic forces can be performed and studied and the next-level, while being accurate at a smaller scale.

Transistors
Due to graphene helices’ superconductivity, transistors can send and receive signals faster. See carbon nanotube field-effect transistor for more.